Dichotomous Coordinate Descent Research Articles

Low-complexity recursive constrained maximum Versoria criterion adaptive filtering algorithm

Linearly-constrained adaptive filtering algorithms have emerged as promising candidates for system estimation. The existing methods such as the constrained least mean square algorithm rely on mean square error based learning, which delivers suboptimal performance under non-Gaussian noise environments. Therefore, the recursive constrained maximum Versoria criterion (RCMVC) algorithm has been derived and is robust against impulsive distortions. Nonetheless, RCMVC suffers from a notable computational overhead stemming from matrix inversion operations. To circumvent this issue, utilizing the weighting method and the dichotomous coordinate descent (DCD) iteration method, this paper derives a low-complexity version of the RCMVC algorithm called DCD-RCMVC, which alleviates the requirement of matrix inversion and enhances the estimation accuracy and robustness against non-Gaussian interference. Furthermore, we also present a comprehensive theoretical analysis of the DCD-RCMVC algorithm, encompassing discussions on its equivalence, convergence properties, and computational complexity. Simulations performed for system identification problems indicate that the DCD-RCMVC algorithm outperforms the existing state-of-art approaches.

Nonlinear acoustic echo cancellation using low-complexity low-rank recursive least-squares algorithms

Adaptive exponential functional link networks (AEFLN) are a type of linear-in-the-parameter nonlinear filters, which have shown enhanced modeling capability for nonlinear systems. However, the convergence speed of traditional AEFLN is generally slow for long impulse responses, hence, AEFLN trained using recursive least-squares becomes an attractive choice to achieve faster convergence. Moreover, huge computational burden of RLS makes it unsuitable in practical applications like echo cancellation. While low complexity versions of RLS are widely available in literature, they still suffer from low convergence speed. To address this issue, we propose a nonlinear acoustic echo cancellation (NAEC) system using AEFLN-RLS, based on the nearest Kronecker product (NKP) decomposition and low-rank approximation technique, which not only reduces computational complexity but also achieves improved convergence speed (especially tracking). To further improve the echo cancellation performance in non-stationary conditions, a variable regularization approach based NKP-AEFLN-RLS system is also proposed. To also reduce the computational complexity further, dichotomous coordinate descent (DCD) updates are incorporated into the proposed NKP-AEFLN-RLS NAEC system and its variable regularization version. Experimental results show the effectiveness of the proposed algorithms, with the variable regularized version of the algorithm using DCD iterations showing the best compromise between convergence capability and lower computational complexity.

Digital Self-Interference Cancellation for Full-Duplex UAV Communication System over Time-Varying Channels

Full-duplex unmanned aerial vehicle (UAV) communication systems are characterized by mobility, so the self-interference (SI) channel characteristics change over time constantly. In full-duplex UAV communication systems, the difficulty is to eliminate SI in time-varying channels. In this paper, we propose a pilot-aid digital self-interference cancellation (SIC) method. First, the pilot is inserted into the data sequence uniformly, and the time-varying SI is modeled as a linear non-causal function. Then, the time-varying SI channel is estimated by the discrete prolate spheroidal basis expansion model (BEM). The error of block edge channel estimation is reduced by cross-block interpolation. The result of channel estimation is convolved with the transmitted data to obtain the reconstructed SI, which is subtracted from the received signal to achieve SIC. The simulation results show that the SIC performance of the proposed method outperforms the dichotomous coordinate descent recursive least square (DCD-RLS) and normalized least mean square (NLMS) algorithms. When the interference to noise ratio (INR) is 25 dB, the performance index normalized least mean square (NMSE) is reduced by 5.5 dB and 4 dB compared with DCD-RLS and NLMS algorithms, which can eliminate SI to the noise floor, and the advantage becomes more obvious as the INR increases.

Efficient Massive MIMO Detection for M-QAM Symbols

Massive multiple-input multiple-output (MIMO) systems significantly outperform small-scale MIMO systems in terms of data rate, making them an enabling technology for next-generation wireless systems. However, the increased number of antennas increases the computational difficulty of data detection, necessitating more efficient detection techniques. This paper presents a detector based on joint deregularized and box-constrained dichotomous coordinate descent (BOXDCD) with iterations for rectangular m-ary quadrature amplitude modulation (M-QAM) symbols. Deregularization maximized the energy of the solution. With the box-constraint, the deregularization forces the solution to be close to the rectangular boundary set. The numerical results demonstrate that the proposed detector achieves a considerable performance gain compared to existing detection algorithms. The performance advantage increases with the system size and signal-to-noise ratio.

Low-Complexity Data-Reuse RLS Algorithm for Stereophonic Acoustic Echo Cancellation

Stereophonic audio devices employ two loudspeakers and two microphones in order to create a bidirectional sound effect. In this context, the stereophonic acoustic echo cancellation (SAEC) setup requires the estimation of four echo paths, each one corresponding to a loudspeaker-to-microphone pair. The widely linear (WL) model was proposed in recent literature in order to simplify the handling of the SAEC mathematical model. Moreover, low complexity recursive least- squares (RLS) adaptive algorithms were developed within the WL framework and successfully tested for SAEC scenarios. This paper proposes to apply a data-reuse (DR) approach for the combination between the RLS algorithm and the dichotomous coordinate descent (DCD) iterative method. The resulting WL-DR-RLS-DCD algorithm inherits the convergence properties of the RLS family and requires an amount of mathematical operations attractive for practical implementations. Simulation results show that the DR approach improves the tracking capabilities of the RLS-DCD algorithm, with an acceptable surplus in terms of computational workload.

Widely nonlinear quaternion-valued second-order Volterra recursive least squares filter

Recently, a family of the quaternion-valued second-order Volterra LMS (QSOV-LMS) algorithms were proposed to deal with 3d and 4d signals. However, it should be noted that the QSOV-LMS algorithms suffer from low convergence speed and high steady-state properties. To this end, a widely nonlinear quaternion recursive least square algorithm is proposed to train the second-order Volterra filter (WNL-QSOVRLS) for enhancing the performance of QSOV-LMS algorithms. Furthermore, to avoid the immense computation complexity, we also present a novel widely nonlinear quaternion Volterra recursive least square dichotomous coordinate descent filtering model (WNL-QSOVRLS-DCD) which introduce the quaternion dichotomous coordinate descent (QDCD) algorithm for the first time. Moreover, based on the augmented model of quaternion second-order Volterra filter, the two proposed algorithms can process quaternion-valued circular and non-circular signals well. Finally, experiments verify the performance of the proposed algorithms.

Recursive constrained generalized maximum correntropy algorithms for adaptive filtering

Thanks to the ability of preventing the accumulation of errors, constrained adaptive filtering (CAF) algorithms have been widely applied. However, in practice, non-Gaussian noise may significantly degrade the filtering performance of CAFs derived from the second-order signal statistics. In this paper, we propose several constrained generalized maximum correntropy (CGMC) algorithms to overcome this problem, inspired by the robustness and flexibility of GMC to non-Gaussian noises. We first introduce a CGMC algorithm based on the gradient method. To improve its convergence rate with correlated inputs, we further propose a recursive CGMC (RCGMC) algorithm. For RCGMC, we conduct the convergence analysis, and characterize the theoretical transient mean square deviation (MSD) performance. Furthermore, we derive a low-complexity version of RCGMC by using the weighting method and the leading dichotomous coordinate descent (DCD) algorithm. Simulation results demonstrate the effectiveness of our proposed algorithms in non-Gaussian noise environment, and the consistency between the analytical and simulation results.

Diffusion maximum versoria criterion algorithms robust to impulsive noise

This paper proposes robust diffusion maximum versoria criterion algorithms to enhance the performance of the distributed estimation in a network of agents under impulsive noise environment. The diffusion maximum versoria criterion is a novel algorithm, under time-dependent constraint on the squared norm of the intermediate update at each node. To develop the robust version of the algorithm, the constraints are calculated by shared information which are collected from connected neighbors. The stability and steady-state performance of the proposed algorithms are also analyzed. We further exploit an altered dichotomous coordinate-descent (DCD) method to improve the performance and to reduce the complexity of the proposed algorithms in shifted-structure input regressors environment. Performance analysis and simulation results show the effectiveness and robustness of the proposed algorithms in various impulsive noise scenarios.

Tensor-Based Recursive Least-Squares Adaptive Algorithms with Low-Complexity and High Robustness Features

The recently proposed tensor-based recursive least-squares dichotomous coordinate descent algorithm, namely RLS-DCD-T, was designed for the identification of multilinear forms. In this context, a high-dimensional system identification problem can be efficiently addressed (gaining in terms of both performance and complexity), based on tensor decomposition and modeling. In this paper, following the framework of the RLS-DCD-T, we propose a regularized version of this algorithm, where the regularization terms are incorporated within the cost functions. Furthermore, the optimal regularization parameters are derived, aiming to attenuate the effects of the system noise. Simulation results support the performance features of the proposed algorithm, especially in terms of its robustness in noisy environments.

Maximum Element Dichotomous Coordinate Descent Based Minimum Variance Distortionless Response DoA Estimator

In this paper, we devise an efficient approach for estimating the direction of arrival (DoA). The proposed DoA estimation approach is based on minimum variance distortionless response (MVDR) criteria within a recursive least squares (RLS) framework. The dichotomous coordinate descent algorithm is used to modify the calculation of the output power spectrum, and a diagonal loading term is applied to improve the robustness of the DoA estimator. These modifications allow us to both reduce the computational complexity of the RLS DoA estimator and increase the estimation performance. A numerical comparison confirms that the proposed DoA estimator outperforms the conventional RLS DoA estimator in terms of the computational complexity and DoA estimation error. Finally, the proposed theoretical DoA estimator is implemented on a field-programmable gate array (FPGA) board to verify the feasibility of the method. The numerical results of a fixed-point implementation demonstrate that the performance of the proposed method is very close to that of its floating-point counterpart.

BEM Adaptive filtering for SI cancellation in full-duplex underwater acoustic systems

Self-interference (SI) cancellation (SIC) is the key technology for achieving full-duplex (FD) communications in underwater acoustic systems. In practice, SI channels are often fast-varying, e.g., due to reflections from surface waves. Classical adaptive filters, such as the recursive least squares (RLS) algorithm, predict the channel impulse response when used for channel estimation. If a tracking delay is acceptable, interpolating estimators capable of providing more accurate estimates of time-varying impulse responses can be used. Interpolating estimators with good tracking performance are normally of high complexity. In this paper, we propose low-complexity interpolating adaptive filters which combine the basis expansion model (BEM) approach with the sliding-window RLS (SRLS) algorithm. Specifically, we use the Legendre polynomials as the basis functions and solve the system of equations using dichotomous coordinate descent (DCD) iterations, thus the name the SRLS-L-DCD adaptive filter. A sparse algorithm (HSRLS-L-DCD) based on homotopy iterations is then proposed to exploit the sparsity in the expansion coefficients. The identification performance of the adaptive filters is investigated by a simulation which mimics an FD lake experiment. Both the simulation and lake experiments show that significant improvement in the SIC performance is achieved with the proposed low-complexity algorithms compared to the classical SRLS algorithm.

A broadband MVDR beamforming core for ultrasound imaging

The Minimum Variance Distortion less Response (MVDR) beamformer is an attractive alternative to conventional delay and sum (DAS) beamformers in medical ultrasound imaging. However, it is not widely employed in medical ultrasound imaging due to its computational complexity. In this paper, we intend to present a novel broadband MVDR beamformer architecture and its implementation for up to 32 channel ultrasound imaging system. The proposed architecture is based on the subarray MVDR and Dichotomous Coordinate Descent (DCD) iteration based adaptive weight computation. A Field Programmable Gate Array (FPGA) based ultrasound system prototype set up is designed, and the proposed MVDR beamforming Core is emulated on the FPGA. The proposed beamforming core could achieve up to 65.5 fps for a 640 x 480 ultrasound frame. The ultrasound system prototype operates at 20 MHz sampling frequency, and the FPGA implementation resulted in approximately 35% of FPGA resources (Xilinx Kintex-7 410T). Image quality comparisons in terms of Contrast Ration (CR) and Contrast to Noise Ratio (CNR) were performed with MATLAB™ MVDR model ported on the Verasonics™ Vantage-64 ultrasound research platform.

DCD-Based Joint Sparse Channel Estimation for OFDM in Virtual Angular Domain

Massive Multiple Input Multiple Output (MIMO) is a promising technique for communications due to the high data transmission rate. To harvest the benefit from the massive MIMO, it is necessary to have accurate channel estimates. Such channels often exhibit sparsity in the virtual angular domain. This paper proposes a dichotomous coordinate descent (DCD) based algorithm for joint sparse channel estimation in the virtual angular domain for the orthogonal-frequency-division-multiplexing massive MIMO. We show that compared to the distributed sparsity adaptive matching pursuit algorithm previously proposed for this purpose, the DCD-based algorithm has significantly lower complexity and better channel estimation performance.

Diffusion recursive total least square algorithm over adaptive networks and performance analysis

In most existing distributed estimation algorithms, many scholars adopted the assumption that the output signal of the system is noisy and the input signal is sufficiently accurate. However, in real applications, the filter input vector usually contains noise. In such situations, it has been proved that the adaptive filtering algorithm using total least squares (TLS) method has shown better performance than classical least squares (LS) method. So in this paper, we propose a diffusion recursive total least squares (DRTLS) algorithm by using the single inverse power iterations in the distributed network. Then, we analyze the mean and mean square behaviors of the proposed DRTLS algorithm. In addition, to reduce the computational complexity of the DRTLS algorithm,an improved algorithm called DCD-DRTLS is also proposed by using the dichotomous coordinate descent (DCD) iterations. At last, simulation results illustrate the superiority of the proposed algorithms and the validity of the theoretical analysis results.

Novel Adaptive Controller for Buck Converter with High Resource Efficiency and Low Computational Complexity

Power converters are used in a wide range of industrial processes. Computational complexity, tracking ability, and calculation accuracy are the main parameters that affect the switching performance of power converters. One of the major parts of switch-mode power converters is the controllers which are essential for proper operation. A new adaptive controller is proposed to reduce the computational complexity, the algorithm is presented based on Improved Variable Forgetting Factor (IVFF), Leading Dichotomous Coordinate Descent (DCD), and Exponentially-weighted Recursive Least Square (ERLS). The proposed method estimates the system coefficients with 98% accuracy. The settling time of the output voltage is 0.008[Formula: see text]ms which is faster than other algorithms. According to Leading DCD, this structure needs no multiplier and divider blocks. VFF leads to the improvement of the tracking ability and convergence rate in the system variations. This structure can be implemented on any application that needs an optimal controller. The Vedic mathematics as a multiplier operation is used in the structure of the improved VFF for reducing the calculation delay and area. The error of the proposed method converges to zero with lower than 60 iterations. In other words, the proposed algorithm calculates the optimal coefficients with lower than 50 iterations and is faster than another algorithm.

Improved Convergence Speed of a DCD-Based Algorithm for Sparse Solutions

To solve a system of equations that needs few updates, such as sparse systems, the leading dichotomous coordinate descent (DCD) algorithm is better than the cyclic DCD algorithm because of its fast speed of convergence. In the case of sparse systems requiring a large number of updates, the cyclic DCD algorithm converges faster and has a lower error level than the leading DCD algorithm. However, the leading DCD algorithm has a faster convergence speed in the initial updates. In this paper, we propose a combination of leading and cyclic DCD iterations, the leading-cyclic DCD algorithm, to improve the convergence speed of the cyclic DCD algorithm. The proposed algorithm involves two steps. First, by properly selecting the number of updates of the solution vector used in the leading DCD algorithm, a solution is obtained from the leading DCD algorithm. Second, taking the output of the leading DCD algorithm as the initial values, an improved soft output is generated by the cyclic DCD algorithm with a large number of iterations. Numerical results demonstrate that when the solution sparsity γ is in the interval [ 1 / 8 , 6 / 8 ] , the proposed leading-cyclic DCD algorithm outperforms both the existing cyclic and leading DCD algorithms for all iterations.

An Efficient Nonlinear Dichotomous Coordinate Descent Adaptive Algorithm Based on Random Fourier Features

The auxiliary normal equation is proposed to construct an incremental update (IU) system in which the increment of weight vector rather than the weight itself is optimized at each iteration, which however, can only deal with problems under linearity assumption. In this letter, we establish the IU system in a fixed-dimension feature space induced by the random Fourier features mapping, enabling it to address nonlinear issues efficiently. Then, to obtain the solution vector to the IU system and overcome high complexity and instability incurred by matrix inversion, a dichotomous coordinate descent (DCD) method is employed to propose an efficient random Fourier features kernel dichotomous coordinate descent (RFFKDCD) algorithm. The proposed RFFKDCD algorithm can tackle nonlinear issues efficiently while avoiding high computational complexity existing widely in kernel-based algorithms. Simulations on both synthetic and real-world examples show that the proposed RFFKDCD algorithm outperforms the recursive least squares-based algorithms in terms of computational load.

Design of AWC core using DCD iterations for MVDR beamformer

This paper presents a hardware architecture using Dichotomous Coordinate Descent (DCD) iterations for Adaptive Weight Computation (AWC) in Minimum Variance Distortionless Response (MVDR) Beamformer. The objective of the proposed work is to achieve low latency and reduced area architecture for the AWC stage in MVDR Beamformer. The work investigates the computation of adaptive weight for 4,8,16 and 32 channels array beamformer. In order to improve the weight updating rate, the existing complex valued cyclic DCD hardware implementation is optimized to 2 clock cycles per iteration. Moreover, DCD algorithm implementation does not require any multiplication and division. The proposed work is implemented on FPGA platform, and the results are compared with state-of-art literature and conclude that the proposed architecture is suitable for MVDR Beamformer employed in high sampling rate applications like medical ultrasound imaging due to its occupancy of a moderate amount of resources and improved processing speed.

DCD-Based Recursive Adaptive Algorithms Robust Against Impulsive Noise

The dichotomous coordinate descent (DCD) algorithm has been successfully used for significant reduction in the complexity of recursive least squares (RLS) algorithms. In this brief, we generalize the application of the DCD algorithm to RLS adaptive filtering in impulsive noise scenarios and derive a unified update formula. By employing different robust strategies against impulsive noise, we develop novel computationally efficient DCD-based robust recursive algorithms. Furthermore, to equip the proposed algorithms with the ability to track abrupt changes in unknown systems, a simple variable forgetting factor mechanism is also developed. Simulation results for channel identification scenarios in impulsive noise demonstrate the effectiveness of the proposed algorithms.

Recursive Least-Squares Algorithms for the Identification of Low-Rank Systems

The recursive least-squares (RLS) adaptive filter is an appealing choice in many system identification problems. The main reason behind its popularity is its fast convergence rate. However, this algorithm is computationally very complex, which may make it useless for the identification of long length impulse responses, like in echo cancellation. Computationally efficient versions of the RLS algorithm, like those based on the dichotomous coordinate descent (DCD) iterations or QR decomposition techniques, reduce the complexity, but still have to face the challenges related to long length adaptive filters (e.g., convergence/tracking capabilities). In this paper, we focus on a different approach to improve the efficiency of the RLS algorithm. The basic idea is to exploit the impulse response decomposition based on the nearest Kronecker product and low-rank approximation. In other words, a high-dimension system identification problem is reformulated in terms of low-dimension problems, which are combined together. This approach was recently addressed in terms of the Wiener filter, showing appealing features for the identification of low-rank systems, like real-world echo paths. In this paper, besides the development of the RLS algorithm based on this approach, we also propose a variable regularized version of this algorithm (using the DCD method to reduce the complexity), with improved robustness to double-talk. Simulations are performed in the context of echo cancellation and the results indicate the good performance of these algorithms.